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I have ran into cracked cylinder heads that can do this. Coolant sits behind the intake valve and when you crank it over, it will smoke and run a little rough then clear up. Pulling the valve cover and oil pan and pressurizing the cooling system was how the problem was found. Being that the crack was in the intake port the boost pressure was enough to keep the coolant in the engine while running, after sitting the coolant would build up behind the valve if the valve was open it would put just enough to sit in the top of the piston. Most of the time with a bad egr cooler you will notice that the pressure in the radiator goes up very quickly if you start the engine while cold, drive it around the shop and park it there will be pressure in the radiator. It's possible that a badly cracked head could cause that as well, but you would be seeing coolant trails from the exhaust manifold/pipes. A quick check of the oil dip stick that revels rust even if the oil doesn't look milky or white is usually a sign of internal leakage. What year of engine is this?